Charge and Spin Transfer Dynamics in a Weakly Coupled Porphyrin Dimer

The dynamics of electron and spin transfer in the radical cation and photogenerated triplet states of a tetramethylbiphenyl-linked zinc-porphyrin dimer were investigated, so as to test the relevant parameters for the design of a single-molecule spin valve and the creation of a novel platform for the photogeneration of high-multiplicity spin states. We used a combination of multiple techniques, including variable-temperature continuous wave EPR, pulsed proton electron–nuclear double resonance (ENDOR), transient EPR, and optical spectroscopy. The conclusions are further supported by density functional theory (DFT) calculations and comparison to reference compounds. The low-temperature cw-EPR and room-temperature near-IR spectra of the dimer monocation demonstrate that the radical cation is spatially localized on one side of the dimer at any point in time, not coherently delocalized over both porphyrin units. The EPR spectra at 298 K reveal rapid hopping of the radical spin density between both sites of the dimer via reversible intramolecular electron transfer. The hyperfine interactions are modulated by electron transfer and can be quantified using ENDOR spectroscopy. This allowed simulation of the variable-temperature cw-EPR spectra with a two-site exchange model and provided information on the temperature-dependence of the electron transfer rate. The electron transfer rates range from about 10.0 MHz at 200 K to about 53.9 MHz at 298 K. The activation enthalpies Δ‡H of the electron transfer were determined as Δ‡H = 9.55 kJ mol–1 and Δ‡H = 5.67 kJ mol–1 in a 1:1:1 solvent mixture of CD2Cl2/toluene-d8/THF-d8 and in 2-methyltetrahydrofuran, respectively, consistent with a Robin–Day class II mixed valence compound. These results indicate that the interporphyrin electronic coupling in a tetramethylbiphenyl-linked porphyrin dimer is suitable for the backbone of a single-molecule spin valve. Investigation of the spin density distribution of the photogenerated triplet state of the Zn-porphyrin dimer reveals localization of the triplet spin density on a nanosecond time scale on one-half of the dimer at 20 K in 2-methyltetrahydrofuran and at 250 K in a polyvinylcarbazole film. This establishes the porphyrin dimer as a molecular platform for the formation of a localized, photogenerated triplet state on one porphyrin unit that is coupled to a second redox-active, ground-state porphyrin unit, which can be explored for the formation of high-multiplicity spin states.


■ INTRODUCTION
−25 These applications raise important questions about how the individual building blocks that form functional mixed valence compounds can be rationally tuned to influence their performance.For example, spin valves typically require 26−31 a high energy barrier between the functional elements (Figure 1), whereas the Pauli spin blockade observed in two-quantum-dot nanoelectronic devices 32−34 requires low tunneling barriers.Lack of understanding of how different linking groups produce different electronic tunneling barriers impedes the rational design of molecular electronic devices, such as spin valves 26−31 or double-dots.It is thus important to study how electronic tunneling barriers can be tuned by chemical design.
Organic mixed valence systems can be classified based on the strength of the electronic coupling between the individual redox sites as proposed by Robin and Day: 35 (i) the electronic coupling between individual sites is negligible and results in localization of the charge (Robin−Day class I); (ii) a moderate electronic coupling results in partially localized charges and the possibility of electron transfers across a barrier between the redox sites (Robin−Day class II); (iii) the strong electronic coupling leads to coherent charge delocalization with a single minimum on the potential energy surface (Robin−Day class III). 2,35−41 On the other hand, many molecular electronics elements require class II systems with reduced electronic coupling.−44 Our proposed prototype molecular spin valve consists of two different paramagnetic metalloporphyrin complexes that are independent single-molecule magnets at low temperature and act as spin polarizer and spin analyzer, creating and reading out a spin-polarized current, respectively (Figure 1b).The different magnetic anisotropy barriers of the paramagnetic metal porphyrin complexes allow for a selective inversion of their magnetic moments and the preferential spin polarization of the conductance electrons by an external magnetic field. 45,46This enables reversible switching between low-resistance and highresistance states.If the sign of the exchange coupling between the metal ions and the conductance electrons is the same for both metalloporphyrin units, low-resistance and high-resistance states are obtained with parallel and antiparallel aligned magnetic moments of the metals, respectively (Figure 1).
The performance of a spin valve is highly dependent on the nature of the linker between the porphyrin complexes, as it must convey sufficient electronic coupling to sustain a current via single-electron transfer events, while preserving the independence of the two magnetic centers.In addition, the height of the tunneling barrier between the two spin centers determines the magnitude of the magnetoresistance. 42The resulting spin valve could be used as a magneto-responsive switch because its electrical resistance is expected to change in response to an external magnetic field, leading to applications as nonvolatile memory devices or for implementing logic operations in single-molecule conductance measurements.
In this work, we have used a combination of variabletemperature continuous wave (cw) EPR spectroscopy, 1 H Mims electron−nuclear double resonance (ENDOR) spectroscopy, optical spectroscopy, and supporting density functional theory (DFT) calculations and simulations to investigate the electronic structure of a tetramethylbiphenyl-linked Znporphyrin dimer mixed valence compound that acts as a model system for the porphyrin backbone of the proposed spin valve.To simulate the electron transfer dynamics in this mixed valence system, we developed a robust approach using pulsed hyperfine spectroscopy to quantify interactions that cannot be resolved by cw-EPR spectroscopy.−50 The spin transfer dynamics of the radical cation mixed valence compound are compared to the dynamics of a photogenerated triplet state on the same porphyrin backbone.Molecular architectures with two decoupled porphyrin sites could be used as platforms for generating high-multiplicity spin states for quantum information processing. 51−57 Therefore, a molecule that allows the formation of a photogenerated triplet state that is weakly coupled to a redox active, tunable, ground-state porphyrin unit with a metal binding site would be a versatile platform for investigating high-multiplicity spin states.In this work, we investigate the delocalization of the photogenerated triplet state in a tetramethylbiphenyl-linked Zn-porphyrin dimer using transient cw-EPR and 1 H Mims ENDOR spectroscopy.Our findings demonstrate that the photogenerated triplet state remains localized on one porphyrin unit, on the EPR time scale, over a wide range of temperatures and in different sample environments.

■ RESULTS AND DISCUSSION
Synthesis and Molecular Design.Porphyrin dimer P2 was designed to feature two redox-active zinc porphyrin units connected via a twisted tetramethyl biphenyl bridge (Scheme 1).Porphyrin monomer P1 was chosen to model a single site of P2.The steric demand of the methyl substituents on the 2,2′,6,6′ positions of the biphenyl groups of P1 and P2 results in a perpendicular orientation of the two phenyl units.−60 Investigation of the dihedral angle distribution between the porphyrin and biphenyl linker in P1 •+ using DFT calculations shows that at 298 K about 75% of the populated geometries have an angle smaller than 25°(see Supporting Information Section 7.1 for details).Therefore, only the lowest energy geometry with a coplanar arrangement of the porphyrin and neighboring phenyl was considered in the analysis of this compound.Two factors lead to a high barrier to charge hopping in P2 •+ : a) the twist in the central biphenyl and b) the fact that the planes of the two porphyrins tend to be orthogonal.Terminal alkyne units were included in P2 so that the dimer could be incorporated into a molecular wire.Bulky 3,5-bis(trihexylsilyl)phenyl substituents were attached to both peripheral meso positions of each porphyrin unit to achieve high solubility and inhibit aggregation.
UV−Visible−NIR Absorption Spectroscopy.Optical spectroscopy of an organic mixed valence system, such as P2 •+ , can provide important information about its reorganization energy, λ, and the electronic coupling, H, between different sites of the molecule and probes the delocalization of the radicals on a femtosecond time scale in solution. 2,8−65 The steady-state absorption spectra of neutral and oxidized P1 Sym , P1, and P2 were measured during an oxidation titration with BAHA in CHCl 3 and are shown in Figure 2. The spectra of neutral P1 Sym , P1, and P2 show a characteristic Q-band absorption with lowest energy absorption bands at 622, 633, and 635 nm, respectively.In the spectra of their respective radical cations, the lowest energy electronic transitions are shifted to 950, 993, and 993 nm, respectively.TD-DFT calculations of the excitation energies of neutral and oxidized P1 Sym , P1, and P2 with LC-ωPBE, ω = 0.1 as functional and Journal of the American Chemical Society the 6-31G* basis set are in good agreement with the experimental observations (Figure 2, vertical bars).−68 The lowest energy absorption bands of P1 Sym •+ , P1 •+ , and P2 •+ mainly arise from HOMO → SOMO transitions and correspond to the P 1 bands of the hole polarons.The slight bathochromic shift of the Q-band absorption of neutral P1 compared to P1 Sym results from an extension of the conjugated π-system by one phenyl group in the biphenyl-porphyrin systems.The lack of a further red-shift of the lowest-energy absorption band of P2 is evidence for the electronic decoupling of the two porphyrin sites by the twisted biphenyl linker.Similarly for the radical cations, the P 1 bands of P1 •+ and P2 •+ are shifted toward longer absorption wavelengths by about 40 nm (ΔE Abs = 0.06 eV) relative to the P 1 band of P1 Sym •+ , which points toward a partial delocalization of the radical cation onto one-half of the biphenyl linker.The identical lowest-energy absorption bands of P1 •+ and P2 •+ stem from the same radical distribution in both systems and demonstrate the localization of the hole on one site of P2 •+ .TD-DFT calculations on P2 •+ predict a very weak (f = 0.0006) intervalence charge transfer (IV-CT) band at 2032 nm, and observation of this band could provide a more in-depth analysis of the electronic structure; however, this band appears to be too broad and weak to be observed experimentally (SI Figure S29 and Table S15).
Continuous Wave EPR.The cw-EPR spectra of the radical cations P1 Sym •+ , P1 •+ , and P2 •+ at 298 K in CD 2 Cl 2 /toluened 8 /THF-d 8 1:1:1 at X-band frequencies are shown in Figure 3.The spectrum of P1 Sym •+ is consistent with previous reports for this radical cation 37 and consists of nine prominent hyperfine lines that arise from an isotropic coupling of 14N A iso = 3.99 MHz to the four equivalent 14 N nuclei, which are further split by an isotropic coupling of 1H A iso = 0.94 MHz to the four equivalent ortho protons of the meso aryl groups.The cw-EPR spectrum of P1 •+ exhibits a partially resolved hyperfine structure that arises from an isotropic coupling of 14N A iso = 3.99 MHz to the four equivalent 14 N nuclei.The 1 H hyperfine coupling pattern is not resolved in this spectrum due to additional hyperfine interactions, which leads to the inhomogeneous broadening of the spectrum.The roomtemperature cw-EPR spectrum of P2 •+ lacks a resolved hyperfine structure and is narrower than the spectrum of P1 •+ .If hyperfine interactions are the main contribution to the spectral envelope and the radical spin density is completely and uniformly distributed over both sites of P2 where B P1 •+ and B P2 •+ are the Gaussian spectral envelope widths of P1 •+ and P2 •+ , respectively.The numerical simulation of the cw-EPR spectrum of P2 •+ following eq 1 with Gaussian and Lorentzian peak-to-peak line width contributions Γ G = 0.14 mT and Γ L = 0.05 mT, identical to those in P1 •+ , is in excellent agreement with the experimental spectrum (Figure 3).The trend in the spectral envelope widths of P1 •+ and P2 •+ is analyzed in Figure S3 of the Supporting Information and shows a good agreement with the Norris relationship in eq 2. This implies fast hopping of the radical spin density over both sites of P2 •+ on the EPR time scale at 298 K.The lack of a bathochromic shift in the NIR absorption spectrum of P2 •+ compared to P1 •+ shows that the apparent spin density distribution is the result of fast reversible intramolecular electron transfers and not coherent delocalization.−74 To obtain insights into the kinetics of reversible intramolecular electron transfer in P2 •+ , the temperature dependence of the cw-EPR spectra of P1 •+ and P2 •+ in CD 2 Cl 2 /toluene-d 8 /THF-d 8 1:1:1 at X-band frequencies was investigated by variable-temperature cw-EPR spectroscopy between 298 and 175 K in fluid solution and at 100 K in a frozen glass (Figure 4).
The variable-temperature cw-EPR spectra of the butadiynelinked porphyrin dimer cation b-P2 •+ were measured as a reference to differentiate between dynamic line shape effects that result from the intramolecular electron transfer in P2 •+ and anisotropic broadening due to slower tumbling at low temperatures (Figure 4e).The size and shape of b-P2 is comparable to P2, and the rotational diffusion times of both molecules are expected to be similar under identical conditions.The investigations of b-P2 •+ by Peeks, Tait, et al. 36 demonstrated coherent delocalization of the radical spin density over both porphyrin units (Robin−Day class III).Therefore, temperature-dependent line width changes in the •+ and P1 •+ were obtained by least-squares fitting of the isotropic 14 N hyperfine interactions 14N A iso , and in the case of P1 Sym •+ the isotropic hyperfine coupling 1H A iso to four equivalent 1 H nuclei using EasySpin. 70Dimer P2 •+ was simulated assuming a complete and uniform distribution of the radical spin density over both sites on the EPR time scale with 14N A iso (P2 The fluid-phase variable-temperature cw-EPR spectra of P1 •+ between 298 and 175 K are virtually identical, indicating that the hyperfine interactions and the intrinsic Lorentzian line widths, Γ L , in P1 •+ are essentially temperature-independent above 175 K.In contrast, the fluid-phase cw-EPR spectra of P2 •+ exhibit a continuous broadening of their spectral envelope with decreasing temperature, which is highlighted by the superimposed variable-temperature cw-EPR spectra of P2 •+ in Figure S7.The cw-EPR spectra of b-P2 •+ are virtually unchanged between 298 and 225 K but show features consistent with anisotropic broadening at 200 and 175 K. Consequently, the broadening of the cw-EPR spectra of P2 •+ between 298 and 225 K can be attributed to a slower rate k ex of the intramolecular electron transfer, whereas at 200 and 175 K exchange broadening and anisotropic broadening both contribute to the line shape.In all fluid-phase measurements in CD 2 Cl 2 /toluene-d 8 /THF-d 8 1:1:1, the spectral envelope of P2 •+ remains narrower than that of P1 •+ , which suggests that the intramolecular electron transfer in P2 •+ remains fast on the EPR time scale.The cw-EPR spectra of P1 •+ and P2 •+ in a frozen glass show anisotropic broadening and are temperature-independent between 150 and 100 K (Figure 4d and SI Figure S5).The identical spectra of P1 •+ and P2 •+ at 100 K demonstrate the localization of the radical electron on one porphyrin unit in P2 •+ on the EPR time scale, which is supported by the simulation of these cw-EPR spectra (SI Figure S8).This localization is probably caused by a combination of the reorganization energy associated with electron transfer, the lack of flexibility of the porphyrin backbone in the frozen solution, and possibly localization of the SbCl 6 − counterion.In contrast, the frozen solution cw-EPR spectral envelope of b-P2 •+ remains narrower than the spectral envelope of P1 Sym

•+
, consistent with coherent delocalization of the radical spin density over both porphyrin units in the dimer. 36he variable-temperature cw-EPR spectra of P1 •+ , P2 •+ , and b-P2 •+ in MTHF are discussed in detail in Section 3.3 of the Supporting Information Similar to the discussion above, the cw-EPR spectra of P1 •+ and b-P2 •+ are virtually temperatureindependent between 298 and 225 K, while the cw-EPR spectra of P2 •+ exhibit increasing exchange broadening with decreasing temperature.All fluid-phase cw-EPR spectra exhibit increasing anisotropic broadening between 200 and 140 K and suggest localization of the radical spin density on one porphyrin unit of P2 •+ on the EPR time scale below 200 K (SI Figure S6).The temperature at which hopping becomes slow in MTHF (200 K) is higher than in CD 2 Cl 2 /toluene-d 8 / THF-d 8 1:1:1 (175 K), due to the increasing viscosity of MTHF 75 and possibly its higher polarity.

H Mims ENDOR Spectroscopy. The anisotropic H hyperfine interactions of PSym
•+ , P1 •+ , and P2 •+ were measured by pulse Mims ENDOR spectroscopy in frozen CD 2 Cl 2 /toluene-d 8 /THF-d 8 1:1:1 at 80 K and Q-band frequencies (Figure 5).Although decomposition of the ENDOR spectra is not feasible due to the large number of nuclei with similar hyperfine interactions, these spectra provide valuable insight into the spin delocalization of the radical cations.In addition, the anisotropic hyperfine interactions are not dynamically averaged in the frozen solvent matrix.Simulation of the ENDOR spectra can therefore be used to obtain information about the 1 H hyperfine interactions that are not resolved due to the inhomogeneous broadening of the room-temperature cw-EPR spectra.In addition, dynamic processes such as polaron migration and electron hopping can occur rapidly on the EPR time scale at room temperature and can contribute to the investigated spin density distribution. 47However, these processes are typically not observed by EPR spectroscopy at cryogenic temperatures in a frozen matrix, which provides a better probe for the instantaneous radical distribution and hyperfine interactions. 36,37he Q-band 1 H Mims ENDOR spectra of P1 Sym

•+
, P1 •+ , and P2 •+ are centered around the proton Larmor frequency, 1H ν L , and split into symmetric peaks by the hyperfine interactions (Figure 5a).This is characteristic of nuclei in the weak coupling limit, The ENDOR spectra of P1 •+ and P2 •+ are virtually identical, which suggests that both radical cations have the same anisotropic proton hyperfine interactions.This is consistent with localization of the radical spin density on one porphyrin unit in P2 •+ on the EPR time scale and provides additional evidence that the radical cation is not coherently delocalized over both porphyrin units.Simulation of the ENDOR spectra of P1 •+ and P2 •+ using DFT-calculated hyperfine tensors is not feasible due to an over-delocalization of the radical spin density from the porphyrin onto the biphenyl part for a wide a range of DFT functionals with different range-separation parameters (SI Figure S9).
To overcome this limitation, we employed the distributed point-dipole model, described in Section 4 of the Supporting Information, to calculate the 1 H hyperfine interactions in P1 •+ from a systematically assigned spin density distribution.In brief, P1 •+ was formally divided into a porphyrin and a biphenyl subunit (Figure 5d).The extent of radical delocalization between the subunits is quantified by the spin density ratio, Δ, which is defined as the fraction of spin density on the porphyrin subunit.The spin density assigned to each subunit is distributed to individual nuclei in agreement with DFT calculations.Variation of the spin density ratio, Δ, allows for the systematic screening of the radical delocalization with a single fitting parameter.The optimal spin density ratio to describe P1 •+ was determined by comparing the experimental 1 H Mims ENDOR spectrum of P1 •+ with a range of simulated spectra using hyperfine tensors, 1H A, calculated via the distributed point dipole model for a series of spin density ratios (SI Figure S12).The best agreement between the experimental and simulated spectra was found for Δ = 96.1%,as judged by the root-mean-square deviation (rmsd) between the two spectra (Figure 5c).The 1 H Mims ENDOR spectra of P1 •+ and P2 •+ were simulated with identical hyperfine tensors, 1H A, obtained for a spin density ratio Δ = 96.1% (Figure 5a).Noticeably, both ENDOR spectra exhibit a resolved shoulder corresponding to a hyperfine interaction of approximately 2.7 MHz that is absent in the spectrum of P1 Sym •+ (Figure 5a; indicated by arrows).The origin of this feature becomes evident from the simulations of the individual hyperfine contributions to the ENDOR spectra (Figure 5a,b).For P1 Sym

•+
, the width of the ENDOR spectrum is determined by the hyperfine interactions to the ortho-protons of the aryl side groups (dark green).Introduction of the biphenyl unit in P1 •+ desymmetrizes the porphyrin and changes the environment around the porphyrin β-protons.This results in a substantial increase of the largest principal component of the anisotropic hyperfine interactions with the β 1 -protons (orange) that determine the width of the ENDOR spectra of P1 •+ and P2 •+ and give rise to the pronounced shoulder.Apart from subtle intensity changes, identical 1 H ENDOR spectra of P1 •+ and P2 •+ are observed in frozen MTHF at 80 K (SI Figure S13).This is important evidence that the hyperfine couplings of both cations are independent of the solvent systems in frozen solution.
Simulation of the Electron Transfer Dynamics.The temperature dependence of the rate constant, k ex , for reversible intramolecular electron transfer in P2 •+ was determined by simulating the variable-temperature cw-EPR spectra of P1 •+ and P2 •+ between 298 and 200 K at X-band frequencies.The best-fit simulations in CD 2 Cl 2 /toluene-d 8 /THF-d 8 1:1:1 are shown in Figure 6.The simulations of P2 •+ were obtained with the electron transfer rates, k ex , in Table 1 with error margins determined as the electron transfer rates with a 5% larger rmsd between the experimental and simulated spectra than the minimum rmsd (SI Figure S18).The experimental and simulated variable-temperature cw-EPR spectra in MTHF are compared in Figure S19.All simulations were performed with a two-site chemical exchange model implemented by Stoll 76 and Kozhanov 77 in MATLAB based on the EasySpin 70 software package in which the radical spin density is distributed over one-half or the other half of P2 •+ (Figure 6a).The magnetic interactions of the unpaired electron with the two redox centers of P2 •+ involved in the intramolecular electron transfer are analogous to the magnetic interactions in P1 •+ and need to be characterized in detail for an accurate simulation of the variable-temperature spectra.The inherent peak-to-peak line width, Γ, of the EPR transitions at each temperature was determined by simulating the cw-EPR spectra of P1 •+ using the chemical exchange model in the slow exchange limit (k ex = 10 −10 MHz) and subsequently used to describe the two redox sites in the simulation of the variable-temperature cw-EPR spectra of P2 •+ at the same temperature.
The characteristic exchange broadening of the cw-EPR spectra of P2 •+ for different electron transfer rates k ex is caused by dynamic changes of the hyperfine interactions.Therefore, simulation of the exchange process requires accurate knowledge of the magnitude of the isotropic hyperfine interaction that are modulated during electron transfer.While the isotopic 14 N hyperfine interactions, 14N A iso , can be obtained from leastsquares fitting of the cw-EPR spectrum of P1 •+ at 298 K, the proton hyperfine couplings are not resolved in the cw-EPR spectra (vide supra).Instead, the 1 H hyperfine interactions were probed by Mims ENDOR spectroscopy and accurately simulated with 1 H hyperfine tensors, 1H A, calculated with the distributed point dipole model for Δ = 96.1%.The five largest isotropic components of these hyperfine tensors in combination with 14N A iso allow an accurate description of the hyperfine interactions modulated during the electron transfer process (SI Figure S16, Table S3).Attempts to simulate the variabletemperature cw-EPR spectra of P1 •+ and P2 •+ using only 14N A iso do not result in a good agreement with the experimental spectra and highlight the importance of the unresolved 1 H hyperfine interactions (see SI Section 6.5).
The reversible intramolecular electron transfer in P2 •+ results in a modulation of the hyperfine interactions, which means that hyperfine couplings to the nuclei on one-half of P2 •+ are accompanied by the absence of couplings to the corresponding nuclei on the other side, and vice versa.Consequently, the symmetry-related nuclei on both sides of P2 •+ are dynamically equivalent with identical time-averaged hyperfine interactions but different instantaneous hyperfine couplings.The effects of a modulation of hyperfine interactions for dynamically equivalent nuclei on the EPR spectrum of a simple model system are discussed in Section 6.2 of the Supporting Information The simulations of the variable-temperature cw-EPR spectra of P2 •+ in CD 2 Cl 2 /toluene-d 8 /THF-d 8 1:1:1 and MTHF quantify the decreasing rate of electron transfer with decreasing temperature.The spectra of P2 •+ between 298 and 225 K can be well simulated with the two-site exchange model, whereas the spectra at 200 K, with contributions of anisotropic broadening to the spectral shape, are no longer well described by the simulations, as evident from the larger root-mean-square deviations and uncertainty boundaries.Therefore, we focus on the temperature range above 200 K in the following analysis.The temperature-dependence of the electron transfer rate k ex between 298 and 225 K in CD 2 Cl 2 /toluene-d 8 /THF-d 8 1:1:1 and MTHF was investigated using the Eyring relationship in eq 3 to determine the activation enthalpy, Δ ‡ H, and activation entropy, Δ ‡ S, that govern the reversible intramolecular electron transfer in P2 •+ : where k B is the Boltzmann constant, R is the molar gas constant, h is Planck's constant, and κ is the electron transmission coefficient. 78,79Plots of ln(k ex T −1 ) versus T −1 for P2 •+ in CD 2 Cl 2 /toluene-d 8 /THF-d 8 1:1:1 and MTHF are shown in Figure 7 and were used to determine Δ ‡ H and Δ ‡ S from the slope and intercept of the trendline between 298 and 225 K, respectively.The kinetic parameters that govern the electron transfer in P2 •+ are given in Table 2.
We used theoretical modeling to estimate the value of the electron transmission coefficient κ.The rate of the electron transfer in P2 •+ is determined by the overlap integral S AB between sites A and B of the two-state chemical exchange process (Figure 6a).The expectation value of the torsion angle Θ between the two phenyl groups of the 2,2′,6,6′-tetramethylbiphenyl linker of P2 •+ and the resulting overlap integral, S AB , were calculated by DFT between 298 and 200 K to investigate the temperature dependence of the electronic coupling between sites A and B (see Supporting Information Section 7.2 for detailed information).In the equilibrium geometry, the two phenyl groups are virtually orthogonal (Θ eq = 90°), resulting in a low overlap integral between the two symmetric charge-localized states.The magnitude of S AB is modulated by changes in the torsion angle, Θ: a broader range of Θ becomes available with increasing temperature, which increases k ex .The extent of coupling between the electron transfer and nuclear vibrations, ν n , was quantified by calculating the electron transmission coefficient following the Landau−Zener approach, which gave κ = 0.035. 80,81The small transmission coefficient (κ ≪ 1) strongly indicates that the electron transfer in P2 •+ occurs in the nonadiabatic regime and proceeds slower than the nuclear motions (κ ex < ν n ).
As expected from Marcus−Hush theory, the electron transfer dynamics in P2 •+ are energetically and dynamically influenced by the polarity of the solvent, resulting in different activation enthalpies and entropies in CD 2 Cl 2 /toluene-d 8 / THF-d 8 1:1:1 and MTHF. 1,82,83Solvation effects contribute to the outer-sphere reorganization energy, λ o , which is often calculated using a dielectric continuum model based on the static dielectric constant, ϵ, and the square of the refractive index, n, of the solvent. 1,84The implicit temperature dependence of λ o and therefore Δ ‡ H due to the temperature dependence of ϵ and n is omitted in our analysis. 85As seen from Table 2, the activation enthalpies, Δ ‡ H, of the intramolecular electron transfer in P2 •+ in CD 2 Cl 2 /toluened 8 /THF-d 8 1:1:1 and MTHF are of the same order of magnitude.The larger activation enthalpy in CD 2 Cl 2 /toluened 8 /THF-d 8 1:1:1 compared to MTHF suggests a higher outer reorganization energy in the mixed solvent system.Further analysis of the solvent effects on the electron transfer dynamics in P2 •+ would require the in-depth characterization of the dielectric properties of the 1:1:1 solvent mixture of CD 2 Cl 2 / toluene-d 8 /THF-d 8 and is beyond the scope of this work.The activation entropies, Δ ‡ S, were calculated for a transmission coefficient κ = 0.035, which approximates the dependence of the intramolecular electron transfer on nuclear vibrations by considering only the change in the biphenyl torsion angle.The negative sign of Δ ‡ S suggests that an ordered transition state of P2 •+ with sufficient electronic coupling between the porphyrin units is required for an efficient electron transfer.
Investigation of the Triplet-State Delocalization.−89 As part of this study, we therefore also investigate the triplet excited state of the porphyrin dimer P2.The transient EPR spectra of 3 P1 Sym , 3 P1, and 3 P2 in MTHF at 20 K and for 3 P1, and 3 P2 in a polyvinylcarbazole (PVK) film at 250 K were averaged between 300 and 400 ns after the  laser pulse with depolarized light excitation at 532 nm and are shown in Figure 8.The spin polarization of all transient EPR spectra does not change significantly over time (SI Figure S32).The AAAEEE polarization pattern (A = absorptive, E = emissive) of the transient EPR spectra indicates a non-Boltzmann population of the triplet sublevels as expected for photogenerated porphyrin triplet states. 90,91This spin polarization arises from different relative intersystem crossing rates to and relaxation rates from the individual triplet sublevels.
The line shapes and widths of the EPR spectra of organic triplets are dominated by their zero-field splitting (ZFS) interactions that arise from the dipolar spin−spin interaction between the two electrons that comprise the triplet and in some cases also from a spin−orbit interaction.Recent work by Moise, Redman, and co-workers has shown that spin−orbit contributions to the zero-field splitting are negligible in Znporphyrins akin to the ones investigated here, and we therefore focus our discussion exclusively on the spin−spin interaction. 92he spin−spin contributions to the zero-field splitting Dtensor can be defined by two ZFS parameters, D and E, where r is the interspin distance, θ is the angle between the zaxis of the molecule and the spin−spin vector, ϕ is the azimuthal angle of the spin−spin vector in the xy-plane, g e is the electronic g-factor, β e is the Bohr magneton, μ 0 is the vacuum permeability, and the angular brackets indicate integration over the triplet wave function. 93,94The magnitudes of D and E are measures of the interspin distance, r, and the orthorhombicity of the spin density distribution, respectively, and determine the distance between the turning points in the transient EPR spectra.These turning points correspond to the canonical orientations of D denoted as X, Y, and Z in Figure 8; the + and − subscripts refer to the m s = 0 ↔ m s = +1 and m s = −1 ↔ m s = 0 transitions, respectively.All other things being equal, an increasing delocalization of the triplet state should result in a reduction of |D|. 91The sign of the D-parameter indicates the orientation of the ZFS tensor in the molecular frame: a positive D-value suggest an oblate spin density (Z-axis of the D-tensor is perpendicular to the porphyrin plane), whereas a negative D-value is consistent with a prolate spin density (Z-axis of D is in the porphyrin plane).
The transient EPR spectrum of 3 P1 Sym in MTHF at 20 K is consistent with previous investigations of the triplet state of this compound by Tait et al. 95,96 The intersystem crossing in Zn-porphyrin monomers is driven by spin−orbit coupling due to mixing of the zinc d-orbitals with the π-system of the porphyrin and results in a preferential population of the out-ofplane sublevel of the triplet state. 97For 3 P1 Sym , this results in a preferential population of the Z sublevel (Table 3).Tait et al. assigned a positive sign to the D-parameter of 3 P1 Sym using magnetophotoselection experiments, which is replicated by DFT calculations at the B3LYP/EPR-II level of theory (Table 4). 95The D-values of biphenyl porphyrins 3 P1 and 3 P2 are similar to |D| for 3 P1 Sym .This suggests a similar triplet-state delocalization in all three systems consistent with a localization of the triplet state on one-half of 3 P2; in other words, there is no evidence for exciton mobility on the EPR time scale.
The 12% increase of |E| for 3 P1 and 3 P2 compared to the value for 3 P1 Sym points toward a higher orthorhombicity of the spin-density distribution.The preferential population of the Z sublevels in 3 P1 and 3 P2 and the position of the hyperfine transitions in the Mims ENDOR spectra (vide inf ra) suggest that the D-tensors of 3 P1 and 3 P2 have approximately the same orientation as in 3 P1 Sym , resulting in a positive D-parameter.The experimental D-values are qualitatively replicated by DFT calculations with B3LYP as functional and the EPR-II basis set that predict approximately identical magnitudes and a positive sign for the D-parameters of 3 P1 Sym , 3 P1, and 3 P2 (Table 4).
The discrepancy between the DFT-calculated spin−spin contributions to the D-parameter and the experimental values is a known limitation for aromatic triplet states. 98,99The trend in DFT-calculated D-parameters for a series of compounds can however inform the interpretation of their experimental spectra. 91,98,99The spin density distributions found in these calculations show a partial delocalization of the triplet spin density onto the biphenyl units of 3 P1 and 3 P2 but no triplet delocalization over both sites of 3 P2 as expected from the experimental data.This localization is consistent with previous reports of localized triplet states in porphyrin nanostructures with a near-orthogonal arrangement of the neighboring porphyrin units at 20 K in MTHF. 100,101To investigate whether the triplet delocalization in 3 P2 can be increased at higher temperatures, the transient EPR spectra of 3 P1 and 3 P2 were measured in a PVK film at 250 K (Figure 8b).The approximately identical D-parameters and spectral widths of 3 P1 and 3 P2 suggest that the triplet state remains localized on one porphyrin unit in 3 P2.The smaller values of |D| in the PVK film compared to MTHF could be the result of slightly different equilibrium geometries in the two environments.The absence of an increasing triplet state delocalization in 3 P2 probably results from a combination of the limited structural flexibility of the porphyrin dimer in the solid film environment and the intrinsically strong coupling between the two electrons comprising the exciton state; in other words, the reorganization energy is too high.
The extent of triplet-state delocalization in 3 P1 Sym , 3 P1, and 3 P2 was further probed using proton hyperfine interactions measured by orientation-selective Mims ENDOR spectroscopy at the canonical field positions X − , Y − , and Z − at 20 K in MTHF (Figure 8c).Previous studies of 3 P1 Sym revealed that the largest hyperfine interactions are observed for the β 1 protons closest to alkyne bonds, consistent with DFT calculations (SI Figure S37). 95,96The transition selection (m s = 0 ↔ m s = +1 or m s = −1 ↔ m s = 0) during the 1 H ENDOR measurements provides information about the relative sign of the hyperfine interaction and the ZFS D-value.In the weak coupling regime, the triplet ENDOR spectrum is asymmetric around the Larmor frequency: in addition to a peak at the Larmor frequency from the T 0 state, for a positive D-value, a second peak is observed at 1H ν L + A i and 1H ν L − A i for the T 0 ↔ T − and T 0 ↔ T + transitions, respectively. 91The sign of the β 1 hyperfine interactions in 3 P1 Sym is negative following the assignment by Tait et al. 95 This is in agreement with DFTcalculated hyperfine tensors at the B3LYP/EPR-II level of theory that also predict negative hyperfine interactions to the β 1 and ortho-biphenyl nuclei in 3 P1 and 3 P2.
The observation of the prominent hyperfine interactions in 3 P1 Sym , 3 P1, and 3 P2 at rf-frequencies smaller than 1H ν L at negative canonical positions is consistent with a positive Dvalue in all investigated systems.Simulations of the 1 H ENDOR spectra of 3 P1 Sym , 3 P1, and 3 P2 using the DFTcalculated hyperfine tensors are broadly in agreement with the experimental spectra, although the magnitude of the hyperfine interactions with nuclei on the biphenyl linker is strongly exaggerated (SI Figure S37).This suggests an overdelocalization of triplet spin density onto the biphenyl linker by DFT, analogous to the over-delocalization of the radical cation spin density (vide supra).The lack of a substantial reduction of the largest hyperfine tensors between 3 P1 and 3 P2 is additional evidence for the localization of the radical spin density on one-half of 3 P2 (SI Figure S36, Table S17).

■ CONCLUSIONS
The electron and spin distribution of the radical cation and photogenerated triplet states of the biphenyl-linked porphyrin  We introduced a robust approach to quantify hyperfine interactions that cannot be resolved by cw-EPR spectroscopy, but are nevertheless crucial to simulate the electron transfer dynamics in P2 •+ , by investigating the 1 H hyperfine interactions of reference compound P1 •+ by 1 H Mims ENDOR spectroscopy and supporting simulations.−50 The kinetic parameters that govern the intramolecular electron transfer in P2 •+ were quantified by investigating the temperature dependence of the electron transfer rate, k ex .The activation enthalpies, Δ ‡ H, that govern the electron transfer in P2 •+ highlight the presence of a large barrier between the porphyrin sites, which is promising for achieving high tunneling magnetoresistance ratios in a molecular spin valve. 42At the same time, the observation of intramolecular electron transfer between the two sites of P2 •+ in CD 2 Cl 2 /toluene-d 8 /THF-d 8 1:1:1 and MTHF suggests that the electronic coupling remains sufficient to sustain an electric current.This makes P2 an excellent candidate for the backbone of a single-molecule spin valve.Future work will focus on the design and synthesis of a heterobimetallic analogue of P2 as a molecular spin valve, by inserting paramagnetic lanthanide cations into the porphyrins and investigating the molecular conductance as a function of magnetic field.Investigation of the spin density distribution of the photogenerated triplet state of P2 using transient EPR spectroscopy and 1 H Mims ENDOR spectroscopy at 20 K in MTHF confirms the localization of the triplet excitons on onehalf of the dimer.This localization is preserved at 250 K in a PVK film, confirming that the orthogonal arrangement of the porphyrin units in P2 prevents the delocalization of the triplet state over a wide range of temperatures and in different sample environments.This makes P2 a versatile platform for the exploration of high-multiplicity spin states by introducing a πradical or paramagnetic metal center such as Cu(II) on the porphyrin unit adjacent to the photogenerated triplet state.
Our results demonstrate that chemical modifications of the electronic coupling in porphyrin nanostructures can be used to control the spin distribution of organic radicals and photogenerated triplet states in a solid matrix: butadiyne-linked porphyrins dimers with strong interporphyrin electronic coupling exhibit coherent delocalization of their radical cations and triplet states in a frozen solution, 36,95,96 whereas the weakly coupled biphenyl-linked porphyrin dimer P2 localizes doublet and triplet spin densities on one porphyrin unit under analogous conditions.Porphyrin nanostructures with weak electronic coupling between individual porphyrin units fulfill important design criteria for novel spintronic materials and are promising as molecular platforms for quantum information processing.
DFT Cartesian coordinates (ZIP) Details on synthetic procedures, spectroscopy, theoretical calculations, data analysis and simulation methods, additional UV−vis−NIR, fluorescence, and EPR spectra, NMR and mass spectra of novel compounds (PDF) ■

Figure 1 .a
Figure 1.a) Scheme of the basic elements of a spin valve, which allows tuning the current (red arrow) that flows through it by the mutual alignment of two magnetic moments (purple and light blue arrows), separated by a barrier (gray).b) Scheme of the molecular unit, with metals in purple and light blue, nitrogens in blue, and carbons color-coded depending on the functional element they belong to, green for the porphyrin elements, gray for the twisted biphenyl barrier.

Figure 2 .
Figure 2. Steady-state UV−vis−NIR absorption spectra of neutral (black) and oxidized (blue) P1 Sym , P1, and P2 in CHCl 3 (298 K).The absorption spectra of the radical cations P1 Sym •+ , P1 •+ , and P2 •+ were obtained by oxidation with one equivalent of BAHA (see SI Figure S27 for the full oxidation titrations).The vertical bars indicate the TD-DFT (LC-ωPBE/6-31G*; ω = 0.1) calculated wavelengths and oscillator strengths, f, for the electronic transitions of the neutral and oxidized compounds in the absence of vibronic coupling.

Figure 5 .
Figure 5. a) Experimental (black) and simulated (red) 1 H Mims ENDOR spectra of P1 Sym •+ , P1 •+ , and P2 •+ recorded at Q-band frequencies in frozen CD 2 Cl 2 /toluene-d 8 /THF-d 8 1:1:1 at 80 K.The spectrum of P1 Sym •+ was simulated using anisotropic 1 H hyperfine tensors, 1H A, obtained from DFT calculations at the B3LYP/EPR-II level of theory.The spectra of P1 •+ and P2 •+ were simulated under identical conditions using hyperfine tensors calculated via the distributed point-dipole model for P1 •+ with a spin density ratio Δ = 96.1%,which is defined as the fraction of spin density on the porphyrin part.The individual contributions to the 1 H ENDOR spectra from the ortho-and β 1 -hydrogens are highlighted in dark green and orange, respectively.b) Schematic representation of the anisotropic 1 H hyperfine tensors of P1 Sym •+ and P1 •+ .The tensors of the ortho-and β 1 -protons that give rise to the highlighted transitions in a) are shown in dark green and orange, respectively; additional tensors are shown in gray as a reference.c) Root-mean-square deviation (rmsd) between the experimental and simulated 1 H Mims ENDOR spectra of P1 •+ as a function of Δ. d) Schematic visualization of the formal separation of P1 •+ into a porphyrin (purple) and biphenyl (blue) fragment.

Figure 6 .
Figure 6.a) Schematic visualization of the redistribution of spin density during the reversible intramolecular electron transfer in P2 •+ .The spin population on each nucleus is represented by a sphere centered on the atom with a radius proportional to the magnitude of its assigned spin population.Red spheres represent excess spin-up and light-blue spheres indicate excess spin-down populations.The torsion angle Θ between the phenyl parts of the tetramethylbiphenyl linker is shown in the inset.Comparison of the experimental (black) and simulated (red) variable-temperature cw-EPR spectra of b) P1 •+ and c) P2 •+ at X-band frequencies in CD 2 Cl 2 /toluene-d 8 /THF-d 8 1:1:1 between 298 and 200 K. Simulations were performed with a two-site chemical exchange model.All monomer spectra were simulated in the slow exchange limit with k ex = 10 −10 MHz.

Figure 8 .
Figure 8.Comparison of the experimental (black) and simulated (red) transient EPR spectra of 3 P1 Sym , 3 P1, and 3 P2 at X-band frequencies in a) MTHF at 20 K and b) a polyvinylcarbazole (PVK) film at 250 K.The experimental spectra are recorded as an average between 300 and 400 ns after the laser pulse with depolarized light excitation at 532 nm.Simulations were performed with the parameters reported in Table 3.The energetic ordering of the principal components of D was chosen as |D Z | > |D X | > |D Y |, and the canonical field positions are indicated (A = absorption, E = emission).c) Experimental 1 H Mims ENDOR spectra of 3 P1 Sym , 3 P1, and 3 P2 recorded at the X − , Y − , and Z − field positions at 20 K in MTHF at X-band frequencies.d) DFT-calculated spin density distributions of 3 P1 Sym , 3 P1, and 3 P2 using the B3LYP functional and the EPR-II basis set.
•+ on the EPR time scale, the theoretical relationship in eqs 1 and 2 established by Norris et al. applies: 69

Table 1 .
Summary of the Electron Transfer Rates k exResulting in the Best-Fit Simulation of the Variable-Temperature cw-EPR Spectra of P2 •+ in CD 2 Cl 2 /Toluened 8 /THF-d 8 1:1:1 a The uncertainties of k ex were determined as the electron transfer rates resulting in root-mean-square deviations (rmsd) 5% larger than the minimum rmsd.The intensity of the experimental and simulated spectra was normalized to calculate the rmsd. a

Table 3 .
Zero-Field Splitting Parameters and Relative Sublevel Populations of 3 P1 Sym , 3 P1, and 3 P2 Determined through Simulation of Their Transient EPR Spectra Presented in Figure8

Table 4 .
Experimental and DFT-Calculated Zero-Field Splitting Parameters for 3 P1 Sym , 3 P1, and 3 P2 P2 were investigated by a combination of EPR and optical spectroscopy, DFT calculations, and theoretical modeling.Fluid-phase variable-temperature cw-EPR spectroscopy of P2 •+ in CD 2 Cl 2 /toluene-d 8 /THF-d 8 1:1:1 and MTHF between 298 and 225 K reveals a thermally activated, intramolecular electron transfer between the two degenerate sites of P2 •+ , consistent with a Robin−Day class II mixed valence compound in the nonadiabatic regime.
AUTHOR INFORMATION the e-INFRA CZ (ID:90140); and the Oxford Advanced Research Computing (ARC) center.For the purpose of Open Access, the author has applied a CC BY public copyright licence to any Author Accepted Manuscript (AAM) version arising from this publication.